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A certain square is to be drawn on a coordinate plane. One [#permalink]

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09 Feb 2007, 00:01

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65% (hard)

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42%(01:24) correct
58%(01:08) wrong based on 137 sessions

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A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

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09 Feb 2007, 00:25

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VirtualM wrote:

From MGMAT. I couldn't understand the explanation...

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

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09 Feb 2007, 00:32

VirtualM wrote:

From MGMAT. I couldn't understand the explanation...

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

A. 4B. 6C. 8D. 10E. 12

Ok giving it more thougt here is what I think are the options:

A(0,0) B(10,0) C(10,10) D(0,10) -1st quadrant

A(0,0) B(-10,0) C(-10,10) D(0,10) -2nd quadrant

A(0,0) B(-10,0) C(-10,-10) D(0,-10) -3rd quadrant

A(0,0) B(10,0) C(10,-10) D(0,-10) -4th quadrant
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11 Feb 2007, 05:00

The issue here is that all coordinates must be integers.

For every quadrant, there is one evident possibility:

(0,0) (10,0) (10,10) (0,10)

But since the lenght of the side is 10, there is one combination of coordinates that generate the same segment: the segment joining points (0,0) and (8,6) since 8^2+6^2=10^2. In a similar way you can build a new square from the segment (0,0) and (6,8).

The reason why with a square with side of 7 or 8 there would only be 4 possibilities is that you cannot have a segment of the same lenght with integers other than (0,7) or (7,0)

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14 Sep 2007, 19:57

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

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14 Sep 2007, 20:32

beckee529 wrote:

ashkrs wrote:

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

A - 4B - 6C - 8D - 10E - 12

I get 8 (C). Two different ways in each of the four regions.

oh shoot.. I think this is a trick question. I change my answer to A (4) because if the set of four squares drawn diagonally cannot generate non-integer coordinates (hence (0, 10sqrt2), etc) we cannot consider those!

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19 Aug 2008, 11:44

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?4681012

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19 Aug 2008, 11:50

I think its A, just because it is a square with area 100, so each side must be 10, it cannot be any other shape than a 10x10 square. so if this is the case, then it can only be drawn four ways, one in each quadrant bc the origin (0,0) has to be one of the vertices. unless I am missing something...